Mathematical Physics, Analysis and Geometry

, Volume 2, Issue 3, pp 291–321 | Cite as

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

  • Lech Zielinski

Abstract

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.

spectral asymptotics Weyl formula self-adjoint elliptic operators with nonsmooth coefficients sharp remainder estimates 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Lech Zielinski
    • 1
  1. 1.Institut de Mathématiques de Paris-Jussieu UMR9994Université Paris 7 (D. Diderot)Paris Cedex 05

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